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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.distribution;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.exception.NotStrictlyPositiveException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.OutOfRangeException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.special.Beta;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.util.ArithmeticUtils;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.random.RandomGenerator;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.random.Well19937c;<a name="line.26"></a>
<FONT color="green">027</FONT>    <a name="line.27"></a>
<FONT color="green">028</FONT>    /**<a name="line.28"></a>
<FONT color="green">029</FONT>     * &lt;p&gt;<a name="line.29"></a>
<FONT color="green">030</FONT>     * Implementation of the Pascal distribution. The Pascal distribution is a<a name="line.30"></a>
<FONT color="green">031</FONT>     * special case of the Negative Binomial distribution where the number of<a name="line.31"></a>
<FONT color="green">032</FONT>     * successes parameter is an integer.<a name="line.32"></a>
<FONT color="green">033</FONT>     * &lt;/p&gt;<a name="line.33"></a>
<FONT color="green">034</FONT>     * &lt;p&gt;<a name="line.34"></a>
<FONT color="green">035</FONT>     * There are various ways to express the probability mass and distribution<a name="line.35"></a>
<FONT color="green">036</FONT>     * functions for the Pascal distribution. The present implementation represents<a name="line.36"></a>
<FONT color="green">037</FONT>     * the distribution of the number of failures before {@code r} successes occur.<a name="line.37"></a>
<FONT color="green">038</FONT>     * This is the convention adopted in e.g.<a name="line.38"></a>
<FONT color="green">039</FONT>     * &lt;a href="http://mathworld.wolfram.com/NegativeBinomialDistribution.html"&gt;MathWorld&lt;/a&gt;,<a name="line.39"></a>
<FONT color="green">040</FONT>     * but &lt;em&gt;not&lt;/em&gt; in<a name="line.40"></a>
<FONT color="green">041</FONT>     * &lt;a href="http://en.wikipedia.org/wiki/Negative_binomial_distribution"&gt;Wikipedia&lt;/a&gt;.<a name="line.41"></a>
<FONT color="green">042</FONT>     * &lt;/p&gt;<a name="line.42"></a>
<FONT color="green">043</FONT>     * &lt;p&gt;<a name="line.43"></a>
<FONT color="green">044</FONT>     * For a random variable {@code X} whose values are distributed according to this<a name="line.44"></a>
<FONT color="green">045</FONT>     * distribution, the probability mass function is given by&lt;br/&gt;<a name="line.45"></a>
<FONT color="green">046</FONT>     * {@code P(X = k) = C(k + r - 1, r - 1) * p^r * (1 - p)^k,}&lt;br/&gt;<a name="line.46"></a>
<FONT color="green">047</FONT>     * where {@code r} is the number of successes, {@code p} is the probability of<a name="line.47"></a>
<FONT color="green">048</FONT>     * success, and {@code X} is the total number of failures. {@code C(n, k)} is<a name="line.48"></a>
<FONT color="green">049</FONT>     * the binomial coefficient ({@code n} choose {@code k}). The mean and variance<a name="line.49"></a>
<FONT color="green">050</FONT>     * of {@code X} are&lt;br/&gt;<a name="line.50"></a>
<FONT color="green">051</FONT>     * {@code E(X) = (1 - p) * r / p, var(X) = (1 - p) * r / p^2.}&lt;br/&gt;<a name="line.51"></a>
<FONT color="green">052</FONT>     * Finally, the cumulative distribution function is given by&lt;br/&gt;<a name="line.52"></a>
<FONT color="green">053</FONT>     * {@code P(X &lt;= k) = I(p, r, k + 1)},<a name="line.53"></a>
<FONT color="green">054</FONT>     * where I is the regularized incomplete Beta function.<a name="line.54"></a>
<FONT color="green">055</FONT>     * &lt;/p&gt;<a name="line.55"></a>
<FONT color="green">056</FONT>     *<a name="line.56"></a>
<FONT color="green">057</FONT>     * @see &lt;a href="http://en.wikipedia.org/wiki/Negative_binomial_distribution"&gt;<a name="line.57"></a>
<FONT color="green">058</FONT>     * Negative binomial distribution (Wikipedia)&lt;/a&gt;<a name="line.58"></a>
<FONT color="green">059</FONT>     * @see &lt;a href="http://mathworld.wolfram.com/NegativeBinomialDistribution.html"&gt;<a name="line.59"></a>
<FONT color="green">060</FONT>     * Negative binomial distribution (MathWorld)&lt;/a&gt;<a name="line.60"></a>
<FONT color="green">061</FONT>     * @version $Id: PascalDistribution.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.61"></a>
<FONT color="green">062</FONT>     * @since 1.2 (changed to concrete class in 3.0)<a name="line.62"></a>
<FONT color="green">063</FONT>     */<a name="line.63"></a>
<FONT color="green">064</FONT>    public class PascalDistribution extends AbstractIntegerDistribution {<a name="line.64"></a>
<FONT color="green">065</FONT>        /** Serializable version identifier. */<a name="line.65"></a>
<FONT color="green">066</FONT>        private static final long serialVersionUID = 6751309484392813623L;<a name="line.66"></a>
<FONT color="green">067</FONT>        /** The number of successes. */<a name="line.67"></a>
<FONT color="green">068</FONT>        private final int numberOfSuccesses;<a name="line.68"></a>
<FONT color="green">069</FONT>        /** The probability of success. */<a name="line.69"></a>
<FONT color="green">070</FONT>        private final double probabilityOfSuccess;<a name="line.70"></a>
<FONT color="green">071</FONT>    <a name="line.71"></a>
<FONT color="green">072</FONT>        /**<a name="line.72"></a>
<FONT color="green">073</FONT>         * Create a Pascal distribution with the given number of successes and<a name="line.73"></a>
<FONT color="green">074</FONT>         * probability of success.<a name="line.74"></a>
<FONT color="green">075</FONT>         *<a name="line.75"></a>
<FONT color="green">076</FONT>         * @param r Number of successes.<a name="line.76"></a>
<FONT color="green">077</FONT>         * @param p Probability of success.<a name="line.77"></a>
<FONT color="green">078</FONT>         * @throws NotStrictlyPositiveException if the number of successes is not positive<a name="line.78"></a>
<FONT color="green">079</FONT>         * @throws OutOfRangeException if the probability of success is not in the<a name="line.79"></a>
<FONT color="green">080</FONT>         * range {@code [0, 1]}.<a name="line.80"></a>
<FONT color="green">081</FONT>         */<a name="line.81"></a>
<FONT color="green">082</FONT>        public PascalDistribution(int r, double p)<a name="line.82"></a>
<FONT color="green">083</FONT>            throws NotStrictlyPositiveException, OutOfRangeException {<a name="line.83"></a>
<FONT color="green">084</FONT>            this(new Well19937c(), r, p);<a name="line.84"></a>
<FONT color="green">085</FONT>        }<a name="line.85"></a>
<FONT color="green">086</FONT>    <a name="line.86"></a>
<FONT color="green">087</FONT>        /**<a name="line.87"></a>
<FONT color="green">088</FONT>         * Create a Pascal distribution with the given number of successes and<a name="line.88"></a>
<FONT color="green">089</FONT>         * probability of success.<a name="line.89"></a>
<FONT color="green">090</FONT>         *<a name="line.90"></a>
<FONT color="green">091</FONT>         * @param rng Random number generator.<a name="line.91"></a>
<FONT color="green">092</FONT>         * @param r Number of successes.<a name="line.92"></a>
<FONT color="green">093</FONT>         * @param p Probability of success.<a name="line.93"></a>
<FONT color="green">094</FONT>         * @throws NotStrictlyPositiveException if the number of successes is not positive<a name="line.94"></a>
<FONT color="green">095</FONT>         * @throws OutOfRangeException if the probability of success is not in the<a name="line.95"></a>
<FONT color="green">096</FONT>         * range {@code [0, 1]}.<a name="line.96"></a>
<FONT color="green">097</FONT>         * @since 3.1<a name="line.97"></a>
<FONT color="green">098</FONT>         */<a name="line.98"></a>
<FONT color="green">099</FONT>        public PascalDistribution(RandomGenerator rng,<a name="line.99"></a>
<FONT color="green">100</FONT>                                  int r,<a name="line.100"></a>
<FONT color="green">101</FONT>                                  double p)<a name="line.101"></a>
<FONT color="green">102</FONT>            throws NotStrictlyPositiveException, OutOfRangeException {<a name="line.102"></a>
<FONT color="green">103</FONT>            super(rng);<a name="line.103"></a>
<FONT color="green">104</FONT>    <a name="line.104"></a>
<FONT color="green">105</FONT>            if (r &lt;= 0) {<a name="line.105"></a>
<FONT color="green">106</FONT>                throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_SUCCESSES,<a name="line.106"></a>
<FONT color="green">107</FONT>                                                       r);<a name="line.107"></a>
<FONT color="green">108</FONT>            }<a name="line.108"></a>
<FONT color="green">109</FONT>            if (p &lt; 0 || p &gt; 1) {<a name="line.109"></a>
<FONT color="green">110</FONT>                throw new OutOfRangeException(p, 0, 1);<a name="line.110"></a>
<FONT color="green">111</FONT>            }<a name="line.111"></a>
<FONT color="green">112</FONT>    <a name="line.112"></a>
<FONT color="green">113</FONT>            numberOfSuccesses = r;<a name="line.113"></a>
<FONT color="green">114</FONT>            probabilityOfSuccess = p;<a name="line.114"></a>
<FONT color="green">115</FONT>        }<a name="line.115"></a>
<FONT color="green">116</FONT>    <a name="line.116"></a>
<FONT color="green">117</FONT>        /**<a name="line.117"></a>
<FONT color="green">118</FONT>         * Access the number of successes for this distribution.<a name="line.118"></a>
<FONT color="green">119</FONT>         *<a name="line.119"></a>
<FONT color="green">120</FONT>         * @return the number of successes.<a name="line.120"></a>
<FONT color="green">121</FONT>         */<a name="line.121"></a>
<FONT color="green">122</FONT>        public int getNumberOfSuccesses() {<a name="line.122"></a>
<FONT color="green">123</FONT>            return numberOfSuccesses;<a name="line.123"></a>
<FONT color="green">124</FONT>        }<a name="line.124"></a>
<FONT color="green">125</FONT>    <a name="line.125"></a>
<FONT color="green">126</FONT>        /**<a name="line.126"></a>
<FONT color="green">127</FONT>         * Access the probability of success for this distribution.<a name="line.127"></a>
<FONT color="green">128</FONT>         *<a name="line.128"></a>
<FONT color="green">129</FONT>         * @return the probability of success.<a name="line.129"></a>
<FONT color="green">130</FONT>         */<a name="line.130"></a>
<FONT color="green">131</FONT>        public double getProbabilityOfSuccess() {<a name="line.131"></a>
<FONT color="green">132</FONT>            return probabilityOfSuccess;<a name="line.132"></a>
<FONT color="green">133</FONT>        }<a name="line.133"></a>
<FONT color="green">134</FONT>    <a name="line.134"></a>
<FONT color="green">135</FONT>        /** {@inheritDoc} */<a name="line.135"></a>
<FONT color="green">136</FONT>        public double probability(int x) {<a name="line.136"></a>
<FONT color="green">137</FONT>            double ret;<a name="line.137"></a>
<FONT color="green">138</FONT>            if (x &lt; 0) {<a name="line.138"></a>
<FONT color="green">139</FONT>                ret = 0.0;<a name="line.139"></a>
<FONT color="green">140</FONT>            } else {<a name="line.140"></a>
<FONT color="green">141</FONT>                ret = ArithmeticUtils.binomialCoefficientDouble(x +<a name="line.141"></a>
<FONT color="green">142</FONT>                      numberOfSuccesses - 1, numberOfSuccesses - 1) *<a name="line.142"></a>
<FONT color="green">143</FONT>                      FastMath.pow(probabilityOfSuccess, numberOfSuccesses) *<a name="line.143"></a>
<FONT color="green">144</FONT>                      FastMath.pow(1.0 - probabilityOfSuccess, x);<a name="line.144"></a>
<FONT color="green">145</FONT>            }<a name="line.145"></a>
<FONT color="green">146</FONT>            return ret;<a name="line.146"></a>
<FONT color="green">147</FONT>        }<a name="line.147"></a>
<FONT color="green">148</FONT>    <a name="line.148"></a>
<FONT color="green">149</FONT>        /** {@inheritDoc} */<a name="line.149"></a>
<FONT color="green">150</FONT>        public double cumulativeProbability(int x) {<a name="line.150"></a>
<FONT color="green">151</FONT>            double ret;<a name="line.151"></a>
<FONT color="green">152</FONT>            if (x &lt; 0) {<a name="line.152"></a>
<FONT color="green">153</FONT>                ret = 0.0;<a name="line.153"></a>
<FONT color="green">154</FONT>            } else {<a name="line.154"></a>
<FONT color="green">155</FONT>                ret = Beta.regularizedBeta(probabilityOfSuccess,<a name="line.155"></a>
<FONT color="green">156</FONT>                        numberOfSuccesses, x + 1.0);<a name="line.156"></a>
<FONT color="green">157</FONT>            }<a name="line.157"></a>
<FONT color="green">158</FONT>            return ret;<a name="line.158"></a>
<FONT color="green">159</FONT>        }<a name="line.159"></a>
<FONT color="green">160</FONT>    <a name="line.160"></a>
<FONT color="green">161</FONT>        /**<a name="line.161"></a>
<FONT color="green">162</FONT>         * {@inheritDoc}<a name="line.162"></a>
<FONT color="green">163</FONT>         *<a name="line.163"></a>
<FONT color="green">164</FONT>         * For number of successes {@code r} and probability of success {@code p},<a name="line.164"></a>
<FONT color="green">165</FONT>         * the mean is {@code r * (1 - p) / p}.<a name="line.165"></a>
<FONT color="green">166</FONT>         */<a name="line.166"></a>
<FONT color="green">167</FONT>        public double getNumericalMean() {<a name="line.167"></a>
<FONT color="green">168</FONT>            final double p = getProbabilityOfSuccess();<a name="line.168"></a>
<FONT color="green">169</FONT>            final double r = getNumberOfSuccesses();<a name="line.169"></a>
<FONT color="green">170</FONT>            return (r * (1 - p)) / p;<a name="line.170"></a>
<FONT color="green">171</FONT>        }<a name="line.171"></a>
<FONT color="green">172</FONT>    <a name="line.172"></a>
<FONT color="green">173</FONT>        /**<a name="line.173"></a>
<FONT color="green">174</FONT>         * {@inheritDoc}<a name="line.174"></a>
<FONT color="green">175</FONT>         *<a name="line.175"></a>
<FONT color="green">176</FONT>         * For number of successes {@code r} and probability of success {@code p},<a name="line.176"></a>
<FONT color="green">177</FONT>         * the variance is {@code r * (1 - p) / p^2}.<a name="line.177"></a>
<FONT color="green">178</FONT>         */<a name="line.178"></a>
<FONT color="green">179</FONT>        public double getNumericalVariance() {<a name="line.179"></a>
<FONT color="green">180</FONT>            final double p = getProbabilityOfSuccess();<a name="line.180"></a>
<FONT color="green">181</FONT>            final double r = getNumberOfSuccesses();<a name="line.181"></a>
<FONT color="green">182</FONT>            return r * (1 - p) / (p * p);<a name="line.182"></a>
<FONT color="green">183</FONT>        }<a name="line.183"></a>
<FONT color="green">184</FONT>    <a name="line.184"></a>
<FONT color="green">185</FONT>        /**<a name="line.185"></a>
<FONT color="green">186</FONT>         * {@inheritDoc}<a name="line.186"></a>
<FONT color="green">187</FONT>         *<a name="line.187"></a>
<FONT color="green">188</FONT>         * The lower bound of the support is always 0 no matter the parameters.<a name="line.188"></a>
<FONT color="green">189</FONT>         *<a name="line.189"></a>
<FONT color="green">190</FONT>         * @return lower bound of the support (always 0)<a name="line.190"></a>
<FONT color="green">191</FONT>         */<a name="line.191"></a>
<FONT color="green">192</FONT>        public int getSupportLowerBound() {<a name="line.192"></a>
<FONT color="green">193</FONT>            return 0;<a name="line.193"></a>
<FONT color="green">194</FONT>        }<a name="line.194"></a>
<FONT color="green">195</FONT>    <a name="line.195"></a>
<FONT color="green">196</FONT>        /**<a name="line.196"></a>
<FONT color="green">197</FONT>         * {@inheritDoc}<a name="line.197"></a>
<FONT color="green">198</FONT>         *<a name="line.198"></a>
<FONT color="green">199</FONT>         * The upper bound of the support is always positive infinity no matter the<a name="line.199"></a>
<FONT color="green">200</FONT>         * parameters. Positive infinity is symbolized by {@code Integer.MAX_VALUE}.<a name="line.200"></a>
<FONT color="green">201</FONT>         *<a name="line.201"></a>
<FONT color="green">202</FONT>         * @return upper bound of the support (always {@code Integer.MAX_VALUE}<a name="line.202"></a>
<FONT color="green">203</FONT>         * for positive infinity)<a name="line.203"></a>
<FONT color="green">204</FONT>         */<a name="line.204"></a>
<FONT color="green">205</FONT>        public int getSupportUpperBound() {<a name="line.205"></a>
<FONT color="green">206</FONT>            return Integer.MAX_VALUE;<a name="line.206"></a>
<FONT color="green">207</FONT>        }<a name="line.207"></a>
<FONT color="green">208</FONT>    <a name="line.208"></a>
<FONT color="green">209</FONT>        /**<a name="line.209"></a>
<FONT color="green">210</FONT>         * {@inheritDoc}<a name="line.210"></a>
<FONT color="green">211</FONT>         *<a name="line.211"></a>
<FONT color="green">212</FONT>         * The support of this distribution is connected.<a name="line.212"></a>
<FONT color="green">213</FONT>         *<a name="line.213"></a>
<FONT color="green">214</FONT>         * @return {@code true}<a name="line.214"></a>
<FONT color="green">215</FONT>         */<a name="line.215"></a>
<FONT color="green">216</FONT>        public boolean isSupportConnected() {<a name="line.216"></a>
<FONT color="green">217</FONT>            return true;<a name="line.217"></a>
<FONT color="green">218</FONT>        }<a name="line.218"></a>
<FONT color="green">219</FONT>    }<a name="line.219"></a>




























































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